"Hi Conrad. You may be wondering how you recorded this message without remembering it. Good question."
Delphine Software is not a famous name in game design. However, their cross-platform hit Another World/Out of this World achieved some noteriety, and their second game, the spiritual successor Flashback: the Quest for Identity, was truly the peak of their game design prowess. (The true sequel to OOTW, OOTW 2: Heart of the Alien was mediocre, and was only released on some doomed platforms to boot.)
Flashback (published on most platforms by US Gold), like its predecessor Out of this World, starts you off lost on a strange world; in this case, the jungles of Titan. Amnesiac and lost, Conrad Hart, the hero, finds himself being briefed by, of all things, a short recording of himself, explaining who to talk to to find out who he is, where he is, and exactly how he got into this predicament. To make a long (although interesting) story short, he finds out that he's a student, his girlfriend is missing, and, oh yeah, there's a force of shapeshifting Unspeakable Horrors threatening the solar system. (In some versions, Conrad is a member of the Galactic Bureau of Investigation; this has little bearing on the plot.)
The gameplay is seriously dated, but very fun if you're willing to deal with the idiosyncracies. Basically, Conrad handles like Blackthorne, although any fan of Out of this World or Prince of Persia will quickly recognize the style of control. (Apparently he's also a distant ancestor of Samus Aran, of Metroid Fusion.) While he's not terribly agile, he has a wide range of moves, quite a few of which will need to be done precisely. He has a tendency to die if he falls too far. Luckily, he's not too bad with machinery or a sidearm, as both are frequently needed in the game's many, many puzzles.
The graphics are also dated, but rather interesting. While the Amiga and CD-based consoles (Jaguar, CD-i, Sega CD, and 3DO) had rather uninteresting rotoscaped interstitial and title screens, the SNES and Genesis versions were blessed with moody, attractive drawn art, obviously heavily influenced by the imagery of Bladerunner. More interesting are the (by modern standards) crude polygonal cut scenes, present even in the 16-bit versions of the game.
What really made this shine, when it was new and even now, was the fluidity and variety of Conrad's movements. He has a surprising number of frames of animation, coupled with a large variety of unique moves, so, while his actual design is crude, watching him move is quite a treat.
Unfortunately, this game is burdened with tedious, die-reload-die-reload-die-reload-solve puzzles, many of which are along the lines of "Trip a tripwire, get electrocuted/melted/shot, reload, jump over tripwire." This is very much not fun. Many of the puzzles are inspired, and there's interesting combat; it's just that there's a whole ton of tedium in between. Be warned.
Given the dated gameplay, this is really only a game for those who feel nostalgic about games like Out of this World or Prince of Persia. Tedius try-and-die puzzles will probably frustrate many gamers to distraction; a shame, given the quality of the game's animation and plot.
If you want to give it a try, the SNES and Genesis versions are fairly common, but your best bet is to play it on a CD-based console, Amiga, or Macintosh. (The PC port was crudely executed and rather terrible.) Do be warned that the Amiga and Mac versions is copy protected. If you can't find a copy, however, you're probably out of luck; some unorthodox uses of the console hardware make this game difficult to emulate.
Flashback was rated K-A by the ESRB, and predates most other rating systems.
Flashback made it to a lot of systems over the years. A comprehensive list...
There was a semi-successful sequel titled Fade To Black.
Ubi Soft has publically discussed bringing this title to the Game Boy Advance, but no release date is set.